Probabilistic constraints on structural lineament best fit plane precision obtained through numerical analysis

Journal of Structural Geology

Volumn 82, Issue , 2016, Pages 37-47

  Seers, Thomas D ^a   Hodgetts, David ^a  

^a UNIVERSITY OF MANCHESTER   (United Kingdom)

Author keywords

DEM; Lineament mapping; Monte Carlo simulation; Remote sensing; Structural orientation; Uncertainty

Indexed keywords

DEGREES OF FREEDOM (MECHANICS); INTELLIGENT SYSTEMS; MONTE CARLO METHODS; POLES; REMOTE SENSING; STRUCTURAL GEOLOGY;

DEM; ORIENTATION DISTRIBUTIONS; PROBABILISTIC CONSTRAINTS; PROBABILISTIC FRAMEWORK; ROTATIONAL DEGREES OF FREEDOM; STRUCTURAL DISCONTINUITY; STRUCTURAL ORIENTATIONS; UNCERTAINTY;

STRUCTURAL ANALYSIS;

EID: 84949256468     PISSN: 01918141     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jsg.2015.11.004     Document Type: Article

References (48)

1. Banerjee S., Mitra S. Remote surface mapping using orthophotos and geologic maps draped over digital elevation models: application to the Sheep Mountain anticline, Wyoming. AAPG Bull. 2004, 88:1227-1237.
2. Barton N. The shear strength of rock and rock joints. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 1976, 255-279. Elsevier.
3. Bemis S.P., Micklethwaite S., Turner D., James M.R., Akciz S., Thiele S.T., Bangash H.A. Ground-based and UAV-Based photogrammetry: a multi-scale, high-resolution mapping tool for structural geology and paleoseismology. J. Struct. Geol. 2014, 69:163-178.
4. Berkowitz B., Adler P.M. Stereological analysis of fracture network structure in geological formations. J. Geophys. Res. Solid Earth (1978-2012) 1998, 103:15339-15360.
5. Bingham C. An antipodally symmetric distribution on the sphere. Ann. Stat. 1974, 1201-1225.
6. Bo G., Dellepiane S., Beneventano G. A locally adaptive approach for interferometric phase noise reduction. Geoscience and Remote Sensing Symposium, 1999. IGARSS'99 Proceedings. IEEE 1999 International 1999, 264-266. IEEE.
7. Brown S.R. Fluid flow through rock joints: the effect of surface roughness. J. Geophys. Res. Solid Earth (1978-2012) 1987, 92:1337-1347.
8. Clemen R.T., Winkler R.L. Combining probability distributions from experts in risk analysis. Risk Anal. 1999, 19:187-203.
9. Collins R.T., Weiss R.S. Vanishing point calculation as a statistical inference on the unit sphere, Computer Vision, 1990. Proceedings, Third International Conference on. IEEE 1990, 400-403.
10. De Sá J.P.M. Applied Statistics Using SPSS, STATISTICA, MATLAB and R: Using SPSS 2007, Statistica, MATLAB, and R. Springer Science & Business Media.
11. Fernández O. Obtaining a best fitting plane through 3D georeferenced data. J. Struct. Geol. 2005, 27:855-858.
12. Fischler M.A., Bolles R.C. Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography. Commun. ACM 1981, 24:381-395.
13. Fisher R. Dispersion on a sphere. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences. The Royal Society 1953, 295-305.
14. Forbes C., Evans M., Hastings N., Peacock B. von Mises Distribution. Statistical Distributions 2011, 191-192. fourth ed.
15. Fournier A., Fussell D., Carpenter L. Computer rendering of stochastic models. Commun. ACM 1982, 25:371-384.
16. Golub G.H., Reinsch C. Singular value decomposition and least squares solutions. Numer. Math. 1970, 14:403-420.
17. Gudmundsson A. Rock Fractures in Geological Processes 2011, Cambridge University Press.
18. Hodgetts D. Laser scanning and digital outcrop geology in the petroleum industry: a review. Mar. Pet. Geol. 2013, 46:335-354.
19. Hoek E. Strength of jointed rock masses. Geotechnique 1983, 33:187-223.
20. Hotelling H. Analysis of a complex of statistical variables into principal components. J. Educ. Psychol. 1933, 24:417.
21. Hua J., Leung C., Ong G., Hong B. Clustering rock discontinuity sets through Gustafson-Kessel (GK) algorithm and validity index. Adv. Earth Environ. Sci. 2014, 189:193.
22. Kirschvink J. The least-squares line and plane and the analysis of palaeomagnetic data. Geophys. J. Int. 1980, 62:699-718.
23. Koike K., Nagano S., Kawaba K. Construction and analysis of interpreted fracture planes through combination of satellite-image derived lineaments and digital elevation model data. Comput. Geosci. 1998, 24:573-583.
24. Lindley D.V. The use of probability statements. Accelerated Life Testing and Experts' Opinions in Reliability 1988, C.A. Clarotti, D.V. Lindley (Eds.).
25. Long J., Witherspoon P.A. The relationship of the degree of interconnection to permeability in fracture networks. J. Geophys. Res. Solid Earth (1978-2012) 1985, 90:3087-3098.
26. Mandelbrot B.B. The Fractal Geometry of Nature 1983, vol. 495:1. WH Freeman and Co., New York. Revised and enlarged edition.
27. Mardia K.V. Statistics of Directional Data 1972.
28. Möller T., Trumbore B. Fast, minimum storage ray-triangle intersection. J. Graph. tools 1997, 2:21-28.
29. Moreau C., Regnoult J.-M., Déruelle B., Robineau B. A new tectonic model for the Cameroon Line, Central Africa. Tectonophysics 1987, 141:317-334.
30. Odling N.E., Gillespie P., Bourgine B., Castaing C., Chiles J.P., Christensen N.P., Fillion E., Genter A., Olsen C., Thrane L., Trice R., Aarseth E., Walsh J.J., Watterson J. Variations in fracture system geometry and their implications for fluid flow in fractured hydrocarbon reservoirs. Pet. Geosci. 1999, 5(4):373-384.
31. Pearson K. LIII. On lines and planes of closest fit to systems of points in space. Lond. Edinb. Dublin Philos. Mag. J. Sci. 1901, 2:559-572.
32. Pewsey A. The large-sample joint distribution of key circular statistics. Metrika 2004, 60:25-32.
33. Power W.L., Tullis T.E. Euclidean and fractal models for the description of rock surface roughness. J. Geophys. Res. Solid Earth (1978-2012) 1991, 96:415-424.
34. Rhén I., Thunehed H., Triumf C.-A., Follin S., Hartley L., Hermansson J., Wahlgren C.-H. Development of a hydrogeological model description of intrusive rock at different investigation scales: an example from south-eastern Sweden. Hydrogeol. J. 2007, 15:47-69.
35. Schoenberg M., Sayers C.M. Seismic anisotropy of fractured rock. Geophysics 1995, 60:204-211.
36. Seers T.D., Hodgetts D. Comparison of Digital Outcrop and Conventional Data Collection Approaches for the Characterization of Naturally Fractured Reservoir Analogues. Geological Society, London, Special Publications 374 2013, SP374. 313.
37. Stone M. The opinion pool. Ann. Math. Stat. 1961, 32:1339-1342.
38. Terzaghi R.D. Sources of error in joint surveys. Geotechnique 1965, 15:287-304.
39. Thuy M., León F.P. Non-linear, shape independent object tracking based on 2D lidar data. Intelligent Vehicles Symposium, 2009 IEEE 2009, 532-537. IEEE.
40. Umili G., Ferrero A., Einstein H. A new method for automatic discontinuity traces sampling on rock mass 3D model. Comput. Geosci. 2013, 51:182-192.
41. Vasuki Y., Holden E.-J., Kovesi P., Micklethwaite S. Semi-automatic mapping of geological structures using UAV-based photogrammetric data: an image analysis approach. Comput. Geosci. 2014, 69:22-32.
42. Wang J., Howarth P.J. Use of the Hough transform in automated lineament. Geosci. Remote Sens. IEEE Trans. 1990, 28:561-567.
43. Watson G.S. Goodness-of-fit tests on a circle. Biometrika 1961, 109-114.
44. Watson G.S. The statistics of orientation data. J. Geol. 1966, 786-797.
45. Woodcock N. Specification of fabric shapes using an eigenvalue method. Geol. Soc. Am. Bull. 1977, 88:1231-1236.
46. Woodcock N., Naylor M.A. Randomness testing in three-dimensional orientation data. J. Struct. Geol. 1983, 5:539-548.
47. Yamaji A., Sato K. Clustering of fracture orientations using a mixed Bingham distribution and its application to paleostress analysis from dike or vein orientations. J. Struct. Geol. 2011, 33:1148-1157.
48. Zuber M.T., Smith D.E., Phillips R.J., Solomon S.C., Neumann G.A., Hauck S.A., Peale S.J., Barnouin O.S., Head J.W., Johnson C.L. Topography of the northern hemisphere of Mercury from MESSENGER laser altimetry. Science 2012, 336:217-220.